拓扑空间上算子半群的吸引子

发布时间：2018-03-12 11:40

本文选题：拓扑空间　切入点：算子半群　出处：《内蒙古大学》2017年硕士论文　论文类型：学位论文

【摘要】：根据Olga Ladyzhenskaya在完备距离空间上定义的算子半群的全局吸引子及全局B-吸引子,将它们推广到Hausdorff拓扑空间上,研究在Hausdorff拓扑空间上算子半群的全局吸引子.我们注意到全局B-吸引子被定义为吸引完备距离空间中每个有界集,而在拓扑空间上没有有界集的定义,故我们采用相对紧集代替距离空间中的有界集定义了全局C-吸引子和采用基本有界集代替有界集定义了全局S-吸引子.且根据基本有界集定义了基本(?)类算子半群.并通过结合拓扑学知识,采用夏道行关于笛卡尔定向集的思想方法和网的收敛的概念,研究极限集,这对给出拓扑空间中算子半群吸引子的相关概念起到了关键作用.本文首先得到了拓扑空间上算子半群的全局吸引子、全局C-吸引子和全局s-吸引子的存在条件.例如,证明了定义在Hausdorff拓扑空间上算子半群{Vt},如果{Vt}有有限的全局吸收集B0,则{Vt}有非空极小的紧不变全局吸引子M =σ-(B0);如果{V1}有相对紧的全局C-吸收集C0,则{V,}有非空极小的紧不变全局C-吸引子MC=σ(C0);如果{Vf}是基本(?)类半群,有基本有界的全局s-吸收集S0,则{Vt}有非空极小的紧不变全局s-吸引子Ms=σ(s0).然后,讨论了极小紧的全局吸引子、极小紧的全局C-吸引子和极小紧的全局s-吸引子存在的充分条件.最后,给出了Hausdorff拓扑空间中极小紧吸引集的连通性定理,得到了这三类全局吸引子的连通性结论.
[Abstract]:According to the global attractor and global attractor of B- operator Olga Ladyzhenskaya is defined in the complete metric space of semigroups, extending them to the Hausdorff topological space, study on the global attractor operator in Hausdorff topological space semigroups. We note that the global attractor B- is defined for each attraction in complete metric spaces and bounded set, and in there is no definition of topological space bounded set, so we adopt relatively compact set instead of distance space bounded set in the definition of the global attractor and C- using basic bounded set instead of bounded set S- and the definition of the global attractor. According to the basic definition of bounded set of basic (?) - Semigroups and through. Combining the topology knowledge concept by Xia's thought about the method and Descartes directed set the convergence, the research limit set, the related concept of attractor Operator Semigroups in topological space are To play a key role. This paper firstly obtained topological space Semigroups of global attractor, conditions for the existence of global attractor and a global attractor of the C- s-. For example, the proof of the Hausdorff topological space of operator semigroup {Vt}, if {Vt} has limited absorbing set B0, then {Vt} has a non empty Compact Minimal invariant global attractor M = sigma (B0); if {V1} has a global C- relatively compact absorption set C0, {V,} has a nonempty minimal invariant global attractor of MC= Sigma C- (C0); if {Vf} is a basic (?) semigroups, a basic global s- sector absorbing collection S0 {Vt}, a non empty minimal invariant global attractor Ms= Sigma s- (S0). Then, discusses the global attractor minimal compact, sufficient conditions for the existence of the global attractor and minimal compact C- minimal compact global s- attractor. Finally, gives the Hausdorff topological space minimum connectivity theorem of compact attractor, The connectedness of the three kinds of global attractors is obtained.

【学位授予单位】：内蒙古大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O189.11

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